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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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Schwartz space of functions with values in a Frechet space

Please see the following reference: Treves' book (Dover edition), page 450, exercise 44.6. this short article by Schwartz: http://www.numdam.org/item/SLS_1953-1954__1__A11_0 and this long version of …
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